Answer :
The point-slope equation for the line that passes through the points (30, 2) and (15, -28) is 2x - y - 58 = 0.
How to find the point-slope equation?
The point-slope equation can be found by using the formula given below:
[tex]y-y_{1} =m( x-x_{1})[/tex]
Here, m is the slope. The value of slope can be found by:
[tex]m =\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
We can find the point-slope equation as shown below:
The points of the line are given to be (30, 2), and (15, -28).
The slope of the line can be found using the formula as shown below:
[tex]m =\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
m = (-28 - 2)/(15 - 30)
m = -30/-15
m = 2
Now, we substitute m = 2 and (x_1, y_1) = (30, 2) in the equation to find the point-slope equation of the line:
y - 2 = 2( x - 30)
y - 2 = 2x - 60
2x - y - 58 = 0
Therefore, we have found that the point-slope equation for the line that passes through the points (30, 2) and (15, -28) is 2x - y - 58 = 0.
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